Studying Parallel Coordinates Under Varying Aspect Ratios

Leon Meka

, Mirjam Kronsteiner

and Johanna Schmidt

1,2 a

Visual Analytics, VRVis GmbH, Austria

Institute of Visual Computing & Human-Centered Technology, TU Wien, Austria

Keywords:

Information Visualization, Parallel Coordinates, Aspect Ratio, Visualization Literacy.

Abstract:

In constraint layout environments like dashboards and multi-view applications, designers have less freedom

in selecting the correct aspect ratios for plots. Especially for web-based, responsive dashboards, designers

have little to no control over the layout and size of the presented plots. The effect of aspect ratios on the

readability of line charts and scatter plots has already been studied. However, more evidence is needed for

parallel coordinates, where line slopes indicate correlations between variables. This paper presents a ﬁrst

step towards understanding the effect of aspect ratios on the readability of parallel coordinates. We present a

statistical analysis of aspect ratio effects and summarize the results of a quantitative user study on user literacy

under different aspect ratios. The statistical analysis revealed that angle parameters stay more homogeneous

when changing the plot size in case landscape orientation is used. The user study showed that human observers

perform well when judging correlation based on the angles under differences between plot width and height.

1 INTRODUCTION

In recent years, dashboard creation has become in-

creasingly popular in data-driven workﬂows in many

applications (Wexler et al., 2017). Dashboards are

regularly used in business intelligence (BI) but have

also entered other domains like healthcare (Zhuang

et al., 2022), infrastructure planning (Matheus et al.,

2020), sports (Goudsmit et al., 2022), and the public

discourse during the pandemic (Zhang et al., 2023).

A dashboard can be deﬁned as a visual display of es-

sential information found in the underlying data to

communicate insights. Dashboards enable the efﬁ-

cient handling and interpretation of vast amounts of

data and provide quick overviews on one screen with-

out the need to scroll or switch views. Dashboard de-

signers consolidate and arrange numbers, metrics, key

performance indicators, and visualizations on a single

screen, allowing users to track data points, monitor

trends, and make informed decisions quickly. Dash-

boards may be but are not required to be interac-

tive (Sarikaya et al., 2019). Interactions may involve

selections, ﬁltering, design adaptations (e.g., chang-

ing color scales), and view customization (e.g., adapt-

ing layout and re-arranging views).

When designing data visualizations, designers can

rely on existing best practices for visualization de-

https://orcid.org/0000-0002-9638-6344

sign (Midway, 2020). Guidelines usually involve sug-

gestions for color choices, visual encodings, and chart

types. Less focus has been put on the size of the plots

since, when designing a single visualization, it is easy

to use as much space as possible. However, when

placing data visualizations inside a dashboard layout,

constraints regarding the available space and shape of

the visualization apply. Users may also be allowed

to change the size and position of views in the dash-

board, leading to other visualizations being adapted

accordingly. In addition, dashboard applications are

increasingly built in a web-based manner to enable

easy, cross-platform access where users do not have

to install any software. Responsive designs for dash-

boards ensure that users can view dashboards on de-

vices with varying screen sizes (Zeng et al., 2024). As

such, web-based settings give designers less control

over the exact layout as it adapts to different screens.

The aspect ratio of a data visualization affects how

quickly users can detect trends and patterns in a data

visualization (see also Figure 1). The aspect ratio is

critical when plotting time series data. In line charts,

trends are judged based on the slope of plotted lines,

which are greatly affected by the aspect ratio of the

graph. As a rule of thumb, researchers already recom-

mended selecting an aspect ratio of a graph by bank-

ing line segments of the graphed data to an angle of 45

degrees (known as banking to 45°) (Cleveland, 1986).

992

Meka, L., Kronsteiner, M. and Schmidt, J.

Studying Parallel Coordinates Under Varying Aspect Ratios.

DOI: 10.5220/0013379300003912

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 20th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2025) - Volume 1: GRAPP, HUCAPP

and IVAPP, pages 992-999

ISBN: 978-989-758-728-3; ISSN: 2184-4321

Figure 1: Parallel coordinates plots with different aspect ratios. Line angles are an essential indicator in parallel coordinate

plots to show positive or negative correlations between variables and variables without any strong correlations. Usually,

parallel coordinates are rendered in a rectangular plot (marked in orange). However, especially in dashboard and multi-view

settings, plots may appear in unexpected aspect ratios (marked in gray).

This rule and later variants based on it (Heer and

Agrawala, 2006) emphasize the importance of con-

sidering aspect ratios when creating a chart, mainly

when lines are used as geometric primitives.

Similar to line charts, parallel coordinates plots

use lines to depict data values. Due to the point-line

duality, data points become polylines when arranging

axes in parallel. Line slopes between two axes play

an important role in parallel coordinates. The visible

line patterns indicate whether we can see a strong pos-

itive correlation (parallel lines) or a strong negative

correlation (X-shape) between two variables (Ware,

2012). Since angles are an important visual indica-

tor in parallel coordinates, researchers have used line

angles to develop matching interaction mechanisms.

Angle-dependent selection mechanisms allow to ﬁl-

ter lines based on their angles (Hauser et al., 2002)

and to select lines based on their slope (Sahann et al.,

2021). Line angles and slope guide the user when ex-

ploring data in parallel coordinates. The effect on the

interpretability of line angles in parallel coordinates

under different aspect ratios has yet to be studied. To

improve the general understanding in this regard, we

• present a statistical analysis of the effect of as-

pect ratios on parallel coordinate plots,

• summarize the outcomes of a quantitative user

study targeted to learn more about the users’ lit-

eracy under different aspect ratios, and

• provide ﬁrst guidelines and ideas for future work.

2 RELATED WORK

Our research addresses the topics of parallel coordi-

nates, dashboard design, and design considerations

regarding aspect ratio.

2.1 Parallel Coordinates

Parallel coordinates are a powerful visualization tech-

nique for representing multi-dimensional data (Kelle-

her and Wagener, 1985). Axis, which are arranged in

parallel, represent data dimensions and data points are

depicted as polylines. Parallel coordinates are widely

used in various ﬁelds, including engineering (Cibul-

ski et al., 2023), material sciences (Rickman, 2018),

and ensemble data (Firat et al., 2023). Johansson

and Forsell (Johansson and Forsell, 2016) presented

an extensive study on different rendering techniques

and evaluated them regarding their usefulness for data

analysis. Parallel coordinates offer a variety of re-

search directions (Heinrich and Weiskopf, 2013) for

improved rendering (e.g., bundling), solving overplot-

ting, and integrating interaction. A full review of

all research results on parallel coordinates, including

bundling techniques and axis reordering, goes beyond

the scope of this paper. We concentrate on visual

structures within and literacy of parallel coordinates

plots. Dasgupta and Kosara (Dasgupta and Kosara,

2010) presented a screen-space metrics to evaluate

parallel coordinates plots. The metric takes visual

Studying Parallel Coordinates Under Varying Aspect Ratios

993

structures like the number of line crossings, crossing

angles, convergence, overplotting, and other features

into account. The best layouting for a plot can be cho-

sen according to this metric. Parallel coordinates lit-

eracy (i.e., the ability to read and interpret the plots)

has been intensively studied by Firat et al. (Firat et al.,

2022). Howe and Purves (Howe and Purves, 2005)

studied the perception of angles and oriented lines in

images. Johansson et al. (Johansson et al., 2008) stud-

ied the ability of humans to perceive patterns in par-

allel coordinates and concluded that a maximum of

11 variables should be used not to overwhelm users

during exploration. Kaur and Karki (Kaur and Karki,

2018) used additional connected views to improve the

readability of parallel coordinates. The effect of vary-

ing aspect ratios on angle perception in parallel coor-

dinates has not been studied yet. Our studies con-

tribute new knowledge on angle perception in par-

allel coordinates under varying aspect ratios.

2.2 Dashboard Design

Dashboards, also called multiple-view visualiza-

tions (Qu and Hullman, 2018), have only lately been

identiﬁed as an essential aspect to study in visualiza-

tion research (Sarikaya et al., 2019). Dashboards are

already ubiquitously used in different domains, espe-

cially business intelligence, but also tourism (Antolini

et al., 2024), social media analysis (Lughbi et al.,

2024), or healthcare (Zhuang et al., 2022). Design-

ing a dashboard requires the consideration of known

guidelines for designing visualizations and layout op-

timization. Summarized as dashboard design pat-

terns (Bach et al., 2023), designers are provided with

design suggestions based on the genre their dash-

board is settled in. Kristiansen et al. (Kristiansen

et al., 2022) provided a semantic snapping approach

to help novice users complete dashboards based on

existing views. Setlur et al. (Setlur et al., 2024) who

developed a heuristics for cooperative dashboard de-

sign. Conrow et al. (Conrow et al., 2023) proposed

a design framework for dashboards for mobility data,

which usually contain geospatial information. Epper-

son et al. (Epperson et al., 2023) suggested a dash-

board authoring system where designers do not need

to create every visualization individually. Chen et

al. (Chen et al., 2021) extracted design patterns from

360 images from previous publications, incorporat-

ing the extracted knowledge into a dashboard de-

sign recommendation system. DMiner (Lin et al.,

2024) is another dashboard recommendation system

based on 854 dashboards that have been crawled on-

line. Dashboard recommendation systems are use-

ful for many applications where designers may not

have a visualization background (Soni et al., 2024).

Increasingly, researchers integrated artiﬁcial intelli-

gence (AI) tools into the dashboard generation pro-

cess (Wu et al., 2022). Ma et al. (Ma et al., 2021)

proposed a deep-learning-based dashboard authoring

system that suggests dashboards based on an image

or a sketch. Other AI-based approaches concentrate

on user intent (Pandey et al., 2023) or intended in-

sights (Deng et al., 2023) when suggesting dashboard

designs. We contribute new guidelines about how

to properly insert a parallel coordinates plot into a

dashboard layout, which future dashboard recom-

mendation approaches may consider.

2.3 Aspect Ratio in Visualization

Design considerations for visualization usually tar-

get color scales, shapes, simplicity, and chart types.

Guidelines for designing effective data visualization

is essential in visualization research not to mislead

viewers (McNutt et al., 2020). In their ﬁfth of the ten

guidelines for effective data visualization, Kelleher

and Wagener (Kelleher and Wagener, 2011) address a

carefully chosen aspect ratio as an important design

consideration, especially for time series data. The

effect of different aspect ratios has been intensively

studied for line plots. As a ﬁrst approach, Cleve-

land (Cleveland, 1986) suggested the banking to 45°

approach, where line segments in a line plot should all

have an angle of 45 degrees. Further approaches built

on this rule and suggested extensions toward consid-

ering both axes (Wang et al., 2018), integrating spec-

tral analysis (Heer and Agrawala, 2006), and comput-

ing a slope ratio estimation (Talbot et al., 2012). Tal-

bot et al. (Talbot et al., 2011) suggested minimizing

the arc length of the data curve in a line plot to ﬁnd the

optimal aspect ratio. Other approaches concentrated

on ﬁnding an optimal aspect ratio for scatter plots.

Fink et al. (Fink et al., 2013) proposed an approach

based on Delauney triangulation of the plot. Wang et

al. (Wang et al., 2019) used the information from the

rendered plot images to compute an optimal aspect

ratio. Wei et al. (Wei et al., 2020) concentrate on the

users’ perception of scatter plots with varying aspect

ratios and identify a linear relationship between geo-

metric changes and introduced bias. Ceja et al. (Ceja

et al., 2021) studied the effect of changing aspect ra-

tios on bar charts and noticed that wide aspect ratios

lead to overestimating bars, and narrow aspect ratios

lead to underestimating bars. We contribute a statis-

tical analysis and results from a quantitative user

study on the effect of changing aspect ratios for

parallel coordinates.

IVAPP 2025 - 16th International Conference on Information Visualization Theory and Applications

994

Figure 2: Clustering results. Clustering all plots according to angle parameters revealed three clusters. The plot on the left

side shows the cluster sizes and depicts that primarily cluster2 can be found in the data. The plot on the right side shows the

distribution of clusters among different aspect ratios. Larger aspect ratios show less variety in cluster distribution.

3 ANGLES UNDER VARYING

ASPECT RATIO

We studied the effect of angles in parallel coordinates

under varying aspect ratios from two different direc-

tions. As a ﬁrst step, we collected statistical infor-

mation on how different aspect ratios affect the dis-

tribution of angles (described in Section 3.1). As a

second approach, we conducted a user study to learn

more about users’ perception of angles under varying

aspect ratios (described in Section 3.2).

3.1 Statistical Analysis

The statistical analysis aimed to study the distribution

of angle parameters under different aspect ratios. We

created a web-based application where it was possi-

ble to load different datasets (stored as CSV ﬁles),

display the dataset in a parallel coordinates plot, and

change the aspect ratio (either by drag-and-drop or by

assigning a speciﬁc ratio). Our application also al-

lowed us to calculate the following angle parameters

for all lines between all axes: (i) average angle, (ii)

minimum angle, (iii) maximum angle, and (iv) sum

of all angles.

We selected a set of datasets for the study to con-

duct a statistical analysis (Table 1). We queried Open

Source repositories like Kaggle

. We left out large

datasets, since plotting all lines in the plot would have

led to overplotting and it would have been impossible

for human observers to identify angles. We also tried

to avoid datasets with a majority of categorical dimen-

sions. Dimensions consisting of only a few categories

(e.g., boolean data) caused particular patterns in the

plot that we wanted to avoid. The datasets we were

interested in contained a manageable number of rows

and columns (i.e., could be rendered without causing

https://kaggle.com

overlaps) and predominantly numerical values.

Table 1: The datasets we used for the statistical analysis

contained a moderate number of columns and rows and only

a small portion of categorical attributes.

Dataset Content Rows Columns

Cereals nutritional information of 80 cereal

brands

80 16

Cars information about different car brands

from the year 2022

199 16

WHO information about development fac-

tors for countries in the world for the

year 2000

193 22

Health data about human subjects that were

evaluated for various health metrics

374 13

The four selected datasets were imported into our

analysis application. We used a collection of normally

distributed values of aspect ratios. For every aspect

ratio we exported an analysis ﬁle for all datasets. The

individual analysis ﬁles were later combined into one

complete dataset. We aimed to ﬁnd groups where the

angle parameters are distributed similarly within the

aspect ratios. We applied k-means clustering on the

angle parameters to ﬁnd aspect ratios with similar be-

havior. Since we had calculated more than one an-

gle parameter, we extended standard k-means clus-

tering to work with multidimensional vectors. The

clustering was performed in Python using the scikit-

learn package. We used the elbow method to esti-

mate the number of clusters, where we calculated the

total within the sum of squares for each k number of

clusters and plotted the result as a line. Furthermore,

the average silhouette and Calinski-Harabasz meth-

ods were applied. The optimal number of clusters was

estimated to be 3 in all cases.

The cluster analysis results are shown in Figure 2.

In the ﬁrst plot, the cluster sizes are depicted. One

particular distribution of angle parameters (cluster2)

was found more often in the data than the other two

Studying Parallel Coordinates Under Varying Aspect Ratios

995

(cluster0 and cluster1). We then plotted the distribu-

tion of clusters among different aspect ratios, shown

in the plot on the right. We calculate the aspect ra-

tio as width divided by height. Smaller aspect ratios

correspond to portrait orientations, while larger ratios

represent landscape orientations. When looking at the

area chart, we can see that larger aspect ratios tend

to have less cluster variety than smaller aspect ratios.

Data points with larger aspect ratios are primarily put

into one cluster (cluster2), which depicts a more uni-

form distribution of angle parameters.

3.2 User Study

In the user study, we aimed to gain more information

on how easy it is for human observers to extract in-

formation about the angles from parallel coordinate

plots under varying aspect ratios. We conducted a

web-based user study asking participants to judge the

correlation between two axes based on the line angles.

3.2.1 User Study Design

In the user study, we only used representations for

two axes with lines in between. We are aware that

this does not show an entire parallel coordinates plot.

However, the focus of the user study was on angles in

particular. Therefore, we wanted to ensure that partic-

ipants focused on the angles and were not distracted

by other axes, maybe confused by the axes in question

with different relationships, or looked elsewhere.

Table 2: The user study parameters from which we, in total,

generated 135 different images to be used in the study.

Correlation # Lines Aspect Ratio

-0.97 to 0.0 to 0.97 100, 200, 300 16:9, 4:3, 1:1, 3:4, 9:16

In total, 57 participants ﬁnished the study. 37 par-

ticipants (65%) were between 25 and 54 years old, al-

though we also had participants within the age group

18 − 24 and 55 − 64. We searched for participants

who already had some experience with data visualiza-

tion. 25 participants (43.8%) were occupied in a com-

pany, 15 participants (26.3%) worked in academia,

15 participants (26.3%) were students, and 2 partic-

ipants selected ’Other’. One-third of the participants

(36.8%) classiﬁed themselves as advanced users of

data visualization, another third (33.3%) said to have

intermediate experience, and the last third (29.8%)

identiﬁed themselves rather as beginners.

Participants were given a link where they could

access the online user study. In the beginning, they

were informed that their data would be kept secure

and only stored anonymously. We assigned a token

Figure 3: User study task. Participants were shown lines be-

tween two variables and had to judge the correlation based

on the line angles. Participants also had to rate their conﬁ-

dence in their answers.

to every participant. After ﬁnishing the study, the re-

sults were imported into a database. Dropouts were

not recorded. After starting the study, participants had

to read an introduction to parallel coordinates, how

positive or negative correlation can be judged based

on the line angles (i.e., X-shape versus parallel lines),

and how a random distribution can be identiﬁed. Par-

ticipants then had to complete 25 tasks with randomly

selected images of parallel coordinates. An example

of one of the 25 tasks that participants had to solve

is shown in Figure 3. Participants also had to record

their conﬁdence on a 4-point Likert scale for every

task. We pre-rendered parallel coordinate axes with

different sizes, aspect ratios, and correlation coefﬁ-

cients. The parameters we varied can be seen in Ta-

ble 2. Participants reported that completing the study

was easy and fast, and they did not report any issues.

3.2.2 Results

The user study results are summarized in Figure 4.

Participants performed best (i.e., achieved the lowest

error rate) for quadratic representations (aspect ratio

1:1). The error rate was also lower for 4:3 and 3:4

representations, as seen on the left side in Figure 4.

With longer (16:9) and more narrow (9:16) settings,

participants started to make more errors. The differ-

ence in the distribution of the correct and incorrect

answers was statistically signiﬁcant for aspect ratios

1:1 and 9:16 (p < 0.0001). The difference was not

statistically signiﬁcant for the other pairs of aspect ra-

tios. The error rate changes according to the corre-

lation value, as shown in Figure 4 on the right side.

Generally, the error rate was lower for negatively cor-

related variables and higher for positively correlated

variables. For negatively and positively correlated

variables, the error rate was lower for strong corre-

lations (< 0.9 and > 0.9). The conﬁdence scores of

the participants were equally distributed for all aspect

ratios. Conﬁdence, similar to error rate, more strongly

depends on the correlation.

IVAPP 2025 - 16th International Conference on Information Visualization Theory and Applications

996

Figure 4: User study results. The ratio between correct and incorrect answers did not reveal big differences between the

tested aspect ratios (left plot). However, participants performed best for quadratic, 4:3, and 3:4 settings. The error rate is also

greatly inﬂuenced by the type of correlation (right plot). The error rate was generally lower for negatively correlated variables

(X-shape), independent of the aspect ratio.

4 RESULTS AND

INTERPRETATION

The statistical analysis revealed that angle parame-

ters stay more consistent among larger aspect ratios.

Aspect ratios were calculated as width divided by

height, so larger aspect ratios refer to landscape ori-

entation. In landscape-oriented plots, the angle pa-

rameters stay more consistent even under changing

sizes, while square or portrait-oriented plots behave

less predictably.

The results of the user study were less signiﬁcant.

The results indicate that human observers’ detection

of angle parameters stays relatively consistent along

aspect ratios between 4:3 and 3:4. For more elongated

settings (16:9 and 9:16), participants started to make

more errors. The error rate is closely related to cor-

relation. Our results conﬁrm earlier studies (Heinrich

and Weiskopf, 2015) where it was stated that nega-

tive correlation leads to a very strong visual pattern

in the plot, in contrast to a less pronounced pattern of

parallel lines in the case of a positive correlation.

For designers and programmers integrating paral-

lel coordinates into dashboards, we can present ﬁrst

preliminary guidelines to rely on. Derived from our

statistical analysis and the user study, we suggest

to rely on landscape orientation and quadratic to

3:4/4:3 settings for the individual variable connec-

tions. Landscape orientations seem less prone to

abrupt changes in the angle parameters when the size

of the plot changes. The error rates of human ob-

servers were satisfactory for quadratic to 3:4/4:3 set-

tings for every two axes connections. In a responsive

or dynamically resizable parallel coordinate view, it

might be preferable only to allow landscape orienta-

tions, if possible.

Our results depict a ﬁrst step towards a better un-

derstanding of properly integrating plots into dash-

board environments. Our study links to previous re-

search results on the banking to 45° rule for line

charts and studies on the effect of aspect ratio on

bar charts and scatterplots (as outlined in Section 2).

We strongly believe that further research is needed to

fully understand the effect of aspect ratios on paral-

lel coordinates and to make solid statements about

the optimal aspect ratio for a given plot. First of

all, we conducted both studies using relatively small

datasets. While this was sufﬁcient to gain ﬁrst results,

we would like to conduct further studies with larger

and more dense datasets. Also, the effect of cate-

gorical values on angle parameters needs to be un-

derstood better. Second, we did not study the effects

of line width, color, and other design decisions on the

perception of angles by human observers. Studies on

the perception of patterns in scatterplots under vary-

ing dot size and opacity exist (Strain et al., 2024), and

we would like to extend this knowledge by studying

similar effects for parallel coordinates.

5 CONCLUSION

We presented preliminary results of a statistical analy-

sis of angle parameters and a user study of the percep-

tion of angles in parallel coordinate plots under vary-

ing aspect ratios. From the statistical analysis, we can

derive that landscape-oriented plots tend to have more

consistent angle parameters even when changing the

plot size. From the user study we can derive that

human observers prefer almost quadratic settings for

the individual variable connections. Based on these

ﬁrst results, we can suggest that dashboard designers

take care that parallel coordinate plots are presented

in landscape orientation.

We were generally surprised about the lack of

perception studies on parallel coordinates. Previous

studies compared the effectiveness of ﬁnding cor-

relations between scatter plots and parallel coordi-

nates (Li et al., 2010), studied the learning effect of

novice users (Siirtola et al., 2009), and identiﬁed bar-

Studying Parallel Coordinates Under Varying Aspect Ratios

997

riers for reading parallel coordinates (Srinivas et al.,

2024). However, profound perception studies of the

depiction of patterns in parallel coordinates under dif-

ferent circumstances are still missing. In the future,

we will continue our research on ﬁnding guidelines

for integrating parallel coordinates into multi-view

and desktop environments.

ACKNOWLEDGEMENTS

VRVis is funded by BMK, BMAW, Styria, SFG, Tyrol

and Vienna Business Agency in the scope of COMET

which is managed by FFG (No. 879730). The work

was funded by the project REINFORCE (FFG, No.

4141421).

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